Berkeley’s new navigation center, which invites homeless people and their families and dogs to live together in a more relaxed environment than a traditional shelter, appears to be already having an impact, according to Mayor Jesse Arreguín’s office.

The center on Second Street in West Berkeley
opened its doors on Tuesday, June 26.
It can hold 45 people at a time, and was full by Friday, July 6, according to Karina Ioffee, the mayor’s director of communications.

More importantly, workers at the Pathways navigation center have already found permanent housing for some of the clients.

“There have already been two move-outs this week, both to permanent housing in Berkeley,” Ioffeewrote to members of the media. “Three more permanent housing move-outs are scheduled for next week. No one has exited back to the streets.”

While staff from BACS, or Bay Area Community Services, and the city of Berkeley have been doing outreach among various encampments, a number of the center’s current clients heard about the services through word of mouth and showed up on their own, said Ioffee.

The navigation center, modeled on those in San Francisco, allows people to come in and sleep next to their partners. They can bring their animals, too. They have access to showers, toilets and washing machines, an eating area and at least one meal a day. There area number of garden-like gathering spaces, as well as a vegetable garden in the back. The center is open 24/7 and people are free to come and go as they please.

Those who are deemed “chronically homeless,” meaning they have been living on the streets for at least a year, are eligible to use the center’s services.

Arreguín and the City Council have made addressing Berkeley’s homeless population a top priority. There are approximately 900 homeless people in the city, most of them African-American, according to surveys. Berkeley has 166 permanent shelter beds as well as another 90 beds in the temporary BESS shelter on Ninth Street.

City officials wanted to provide a space where those living on the streets could find respite and also be surrounded by social services that could ultimately transition them to permanent housing. The city is spending $2.44 million this year for the navigation center, both to construct it and to run it.

Arreguín’s officer released these numbers about where those living in the center came from:

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No, of course the natural number can't be summed.
1
+
2
+
3
+
…
has no sum; or we might just as well say that it sums to infinity. The real question is: why do some people write
1
+
2
+
3
+
…
=
−
1
/
12
? The answer involves some maths, some physics, and some analysis of common misunderstandings about what mathematicians and physicists are saying. Some physicists mistakenly believe that mathematicians have summed the series to give
−
1
/
12
. And some mathematicians mistakenly believe that physicists have summed the series experimentally to give
−
1
/
12
. Neither are right, but so much finger pointing of each to the other's discipline has occurred that many laymen now believe that maths
and
physics have both proved that the sum is
−
1
/
12
. The subject is an old one, but gained a new lease of life in 2014 with the appearance of a notorious youtube clip presented by an academic well outside his zone of expertise, who proved only that breaking the rules of elementary maths in the age of the Internet can bring you 15 minutes of fame.

The Relevant Maths

Of course, it's physically impossible to use a calculator, abacus, or pen and paper to actually sum a series that is infinitely long, so mathematicians long ago realised that such an expression must be carefully defined for it to have any useful meaning. They define it in a way that matches everyone's expectation of what such an expression
should
mean: begin the addition term by term in the order written, and keep an eye on the running sum (also known as the "sequence of partial sums") as each term is added. If this running sum gets ever closer to some number, then that number will be unique and is called the sum of the series. If the running sum doesn't behave in that way, then we say the series has no sum. If you start with 1, then add 2 (running sum is 3), then add 3 (running sum is 6), then add 4 (running sum is 10), those partial sums 1, 3, 6, 10, get bigger and bigger and don't get arbitrarily close to any number at all. So the series
1
+
2
+
3
+
…
has no sum. But you knew that anyway.

But didn't the mathematicians Euler and Ramanujan sum the series to give
−
1
/
12
? Ramanujan's letter of almost a century ago to the mathematician Hardy, in which he wrote the sum, dates from a different time. Euler's interest was similar to that of Ramanujan: he wanted to see where the rules of mathematics could take him, so he assumed that the sum existed and performed some mathematical gymnastics to arrive at
−
1
/
12
. Euler and Ramanujan certainly had their feet on the ground enough to know that putting one orange into a big pit, followed by 2 more oranges, then 3 more oranges, and so on forever, is not going to result in there being
−
1
/
12
oranges in the pit. They were trailblazers of other times, and they went very far by experimenting with the fewer boundaries that existed back then. Since that time, proper boundaries have been drawn, and modern mathematics knows perfectly well where these lie: those boundaries were established by setting axiomatic properties of numbers: these properties keep mathematics from running off the rails and all hell breaking loose. Euler's early work belongs to his time and is part of mathematical history. He was allowed to do what he did, but modern mathematicians and physicists no longer work under the paradigm that was current in Euler's time. They now work under established rules that weren't available to Euler.

Tables of content are generated automatically and are based on records of articles contained that are available in the TIB-Portal index. Due to missing records of articles, the volume display may be incomplete, even though the whole journal is available at TIB.

Anna Larsson appeared as Erda with appropriately earthly, burnished tones. Kwangchul Youn’s potent bass was a high point of the evening as Fasolt, although the stage director’s decision to cast shadows behind the giants to imply their size seemed disconnected from the drama. Timo Rihonen was an appropriately menacing Fafner.

Marco Jentzsch brought a youthful, ringing tenor to the role of Froh, and Jan Buchwald’s enveloping voice was well-suited to Donner. Wolfgang Ablinger-Sperrhacke was a theatrically engaging Mime. Aga Mikolaj, Maria Gortsevskaya, and Marina Prudenskaja created a seductive and musically solid ensemble as the Rheinmaidens.

Daniel Barenboim, a champion of Wagner who has conducted the “Ring” for over twenty years, overcame the somewhat dampened acoustics in the Schiller Theater’s unusually deep orchestra pit by bringing forth finely articulated phrases from the
Staatskapelle
. He evoked vivid musical landscapes, from elemental rumblings to ethereal mists, although the brass players showed moments of hesitation in the final scene. The strings gleamed throughout the evening without overwhelming the singers.

Choreography by Sidi Larbi Cherkaoui relied upon undulating motions to mirror the characters’ inner life or create a framework for the action. At times, the dancing effectively heightened the drama, particularly during orchestral interludes that were masterfully shaped by Barenboim; at others, the sequences appeared directionless and haphazard. Alberich’s pivotal transformation into a toad, effected through crouching movement along with the dancers of the Eastman Company who had formed an impressive pyramid of mostly nude bodies behind him, added a naturalistic touch.

The staging’s culmination in a projection of Jef Lambeaux’s marble relief
Human Passions
depicting writhing, twisted bodies seemed to provide continuity with the convoluted human movement woven throughout the opera. The image also may forecast the impending chaos in the godly realm, Valhalla, where the deities return at the end of “Das Rheingold.” Loge danced and splashed onstage in jest before joining them, reaffirming that he had stolen the show.

The production runs through October 31.

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